We present some conditions for the existence and uniqueness of almost automorphic solutions of third order neutral delay-differential equations with piecewise constant of the form（X（t） ＋px（t - 1））″′, = a0x（...We present some conditions for the existence and uniqueness of almost automorphic solutions of third order neutral delay-differential equations with piecewise constant of the form（X（t） ＋px（t - 1））″′, = a0x（[t]） ＋ a1x（[t - 1]） ＋ f（t）,where [.] is the greatest integer function, p, a0 and al are nonzero constants, and f（t） is almost automorphic.展开更多
In this paper,we use a unified framework to study Poisson stable(including stationary,periodic,quasi-periodic,almost periodic,almost automorphic,Birkhoff recurrent,almost recurrent in the sense of Bebutov,Levitan almo...In this paper,we use a unified framework to study Poisson stable(including stationary,periodic,quasi-periodic,almost periodic,almost automorphic,Birkhoff recurrent,almost recurrent in the sense of Bebutov,Levitan almost periodic,pseudo-periodic,pseudo-recurrent and Poisson stable)solutions for semilinear stochastic differential equations driven by infinite dimensional L′evy noise with large jumps.Under suitable conditions on drift,diffusion and jump coefficients,we prove that there exist solutions which inherit the Poisson stability of coefficients.Further we show that these solutions are globally asymptotically stable in square-mean sense.Finally,we illustrate our theoretical results by several examples.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11271380,11501238)Natural Science Foundation of Guangdong Province(Grant Nos.2014A030313641,2016A030313119,S2013010013212)the Major Project Foundation of Guangdong Province Education Department(No.2014KZDXM070)
文摘We present some conditions for the existence and uniqueness of almost automorphic solutions of third order neutral delay-differential equations with piecewise constant of the form（X（t） ＋px（t - 1））″′, = a0x（[t]） ＋ a1x（[t - 1]） ＋ f（t）,where [.] is the greatest integer function, p, a0 and al are nonzero constants, and f（t） is almost automorphic.
基金Supported by NSFC(Grant Nos.11522104,11871132 and 11925102)Xinghai Jieqing and DUT19TD14 funds from Dalian University of Technology。
文摘In this paper,we use a unified framework to study Poisson stable(including stationary,periodic,quasi-periodic,almost periodic,almost automorphic,Birkhoff recurrent,almost recurrent in the sense of Bebutov,Levitan almost periodic,pseudo-periodic,pseudo-recurrent and Poisson stable)solutions for semilinear stochastic differential equations driven by infinite dimensional L′evy noise with large jumps.Under suitable conditions on drift,diffusion and jump coefficients,we prove that there exist solutions which inherit the Poisson stability of coefficients.Further we show that these solutions are globally asymptotically stable in square-mean sense.Finally,we illustrate our theoretical results by several examples.
